A094085 -id:A094085 - cp's OEIS frontend

A204623 Number of (n+1)X2 0..2 arrays with every 2X2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

12, 96, 768, 6144, 49152, 393216, 3145728, 25165824, 201326592, 1610612736, 12884901888, 103079215104, 824633720832, 6597069766656, 52776558133248, 422212465065984, 3377699720527872, 27021597764222976, 216172782113783808

Offset: 1

R. H. Hardin Jan 17 2012

nonn

Column 1 of A204630

			Some solutions for n=3
..0..0....0..0....0..0....0..0....0..1....0..0....0..0....0..0....0..0....0..1
..0..1....1..2....0..1....0..1....2..1....1..1....0..1....0..1....0..1....1..1
..2..2....0..2....0..1....1..2....2..0....2..0....1..1....0..0....2..1....1..2
..0..2....2..1....0..1....2..2....0..1....0..1....1..2....2..1....0..2....1..2

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A094085, A270568.

Empirical: a(n) = 8*a(n-1)

A270568 Expansion of g.f. (1+4x)/(1-8x).

Original entry on oeis.org

1, 12, 96, 768, 6144, 49152, 393216, 3145728, 25165824, 201326592, 1610612736, 12884901888, 103079215104, 824633720832, 6597069766656, 52776558133248, 422212465065984, 3377699720527872, 27021597764222976, 216172782113783808, 1729382256910270464, 13835058055282163712

Offset: 0

Colin Barker, Mar 19 2016

Partial sums are 1, 13, 109, 877, 7021, 56173, ...

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8).

Cf. A001018 (powers of 8), A094085, A204623.

CoefficientList[Series[(1 + 4 x)/(1 - 8 x), {x, 0, 20}], x] (* Michael De Vlieger, Mar 19 2016 *)
Join[{1},NestList[8#&,12,30]] (* Harvey P. Dale, Oct 05 2022 *)

PARI
```
Vec((1+4*x)/(1-8*x) + O(x^30))
```

G.f.: (1+4*x)/(1-8*x).
a(n) = 8*a(n-1) for n>1.
a(n) = 12*8^(n-1) for n>0.
a(n) = A094085(n), n>1. - R. J. Mathar, Mar 21 2016
E.g.f.: (3*exp(8*x) - 1)/2. - Elmo R. Oliveira, Mar 25 2025

cp's OEIS Frontend

A204623 Number of (n+1)X2 0..2 arrays with every 2X2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

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A270568 Expansion of g.f. (1+4x)/(1-8x).

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cp's OEIS Frontend

A204623 Number of (n+1)X2 0..2 arrays with every 2X2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

Views

Author

Keywords

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Examples

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Crossrefs

Formula

A270568 Expansion of g.f. (1+4*x)/(1-8*x).

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Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A270568 Expansion of g.f. (1+4x)/(1-8x).